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<div class="title">LDLT.h</div>  </div>
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<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2008-2011 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2009 Keir Mierle &lt;mierle@gmail.com&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// Copyright (C) 2009 Benoit Jacob &lt;jacob.benoit.1@gmail.com&gt;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Copyright (C) 2011 Timothy E. Holy &lt;tim.holy@gmail.com &gt;</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#ifndef EIGEN_LDLT_H</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#define EIGEN_LDLT_H</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> UpLo_&gt; <span class="keyword">struct </span>traits&lt;LDLT&lt;MatrixType_, UpLo_&gt; &gt;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;   : traits&lt;MatrixType_&gt;</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;  {</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;    <span class="keyword">typedef</span> MatrixXpr XprKind;</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <span class="keyword">typedef</span> SolverStorage StorageKind;</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;    <span class="keyword">typedef</span> <span class="keywordtype">int</span> StorageIndex;</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    <span class="keyword">enum</span> { Flags = 0 };</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;  };</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> UpLo&gt; <span class="keyword">struct </span>LDLT_Traits;</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160; </div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;  <span class="comment">// PositiveSemiDef means positive semi-definite and non-zero; same for NegativeSemiDef</span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  <span class="keyword">enum</span> SignMatrix { PositiveSemiDef, NegativeSemiDef, ZeroSign, Indefinite };</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;}</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html">   61</a></span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> UpLo_&gt; <span class="keyword">class </span><a class="code" href="classEigen_1_1LDLT.html">LDLT</a></div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        : <span class="keyword">public</span> <a class="code" href="classEigen_1_1SolverBase.html">SolverBase</a>&lt;LDLT&lt;MatrixType_, UpLo_&gt; &gt;</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;{</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1SolverBase.html">SolverBase&lt;LDLT&gt;</a> <a class="code" href="classEigen_1_1SolverBase.html">Base</a>;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    <span class="keyword">friend</span> <span class="keyword">class </span><a class="code" href="classEigen_1_1SolverBase.html">SolverBase</a>&lt;<a class="code" href="classEigen_1_1LDLT.html">LDLT</a>&gt;;</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160; </div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;    EIGEN_GENERIC_PUBLIC_INTERFACE(<a class="code" href="classEigen_1_1LDLT.html">LDLT</a>)</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;    <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;      MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;      MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime,</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;      UpLo = UpLo_</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    };</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1&gt;</a> <a class="code" href="classEigen_1_1Matrix.html">TmpMatrixType</a>;</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160; </div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Transpositions.html">Transpositions&lt;RowsAtCompileTime, MaxRowsAtCompileTime&gt;</a> <a class="code" href="classEigen_1_1Transpositions.html">TranspositionType</a>;</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationMatrix&lt;RowsAtCompileTime, MaxRowsAtCompileTime&gt;</a> <a class="code" href="classEigen_1_1PermutationMatrix.html">PermutationType</a>;</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160; </div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    <span class="keyword">typedef</span> internal::LDLT_Traits&lt;MatrixType,UpLo&gt; Traits;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a9ab5fbbe154dd5b43fe272126d69411f">   87</a></span>&#160;    <a class="code" href="classEigen_1_1LDLT.html#a9ab5fbbe154dd5b43fe272126d69411f">LDLT</a>()</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;      : m_matrix(),</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;        m_transpositions(),</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;        m_sign(internal::ZeroSign),</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;        m_isInitialized(false)</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    {}</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160; </div>
<div class="line"><a name="l00100"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#abd3c8856337dfc7f4df6214b9503dcf2">  100</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1LDLT.html#abd3c8856337dfc7f4df6214b9503dcf2">LDLT</a>(<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> <a class="code" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>)</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;      : m_matrix(<a class="code" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>, <a class="code" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>),</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;        m_transpositions(<a class="code" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>),</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;        m_temporary(<a class="code" href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">size</a>),</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;        m_sign(internal::ZeroSign),</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;        m_isInitialized(false)</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    {}</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160; </div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00115"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#ab45453a84ebb985cb0d1d9128b7af18d">  115</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1LDLT.html#ab45453a84ebb985cb0d1d9128b7af18d">LDLT</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix)</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;      : m_matrix(matrix.rows(), matrix.cols()),</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;        m_transpositions(matrix.rows()),</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;        m_temporary(matrix.rows()),</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;        m_sign(internal::ZeroSign),</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;        m_isInitialized(false)</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;    {</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;      compute(matrix.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>());</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;    }</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160; </div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00132"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#ad2f39b7a2a17c6e982db2e4164b6dd9f">  132</a></span>&#160;    <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1LDLT.html#ad2f39b7a2a17c6e982db2e4164b6dd9f">LDLT</a>(<a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix)</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;      : m_matrix(matrix.<a class="code" href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>()),</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;        m_transpositions(matrix.rows()),</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;        m_temporary(matrix.rows()),</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;        m_sign(internal::ZeroSign),</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;        m_isInitialized(false)</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    {</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;      compute(matrix.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>());</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    }</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160; </div>
<div class="line"><a name="l00145"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a3ed6b348086c7b4c117dbff35be1a16d">  145</a></span>&#160;    <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1LDLT.html#a3ed6b348086c7b4c117dbff35be1a16d">setZero</a>()</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    {</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;      m_isInitialized = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    }</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160; </div>
<div class="line"><a name="l00151"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#ae8be83b613c7fad1ad5d0a2b44c483e0">  151</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">typename</span> Traits::MatrixU <a class="code" href="classEigen_1_1LDLT.html#ae8be83b613c7fad1ad5d0a2b44c483e0">matrixU</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LDLT is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;      <span class="keywordflow">return</span> Traits::getU(m_matrix);</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;    }</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160; </div>
<div class="line"><a name="l00158"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a1c29cf5110c180a8fc5da40096822ed1">  158</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">typename</span> Traits::MatrixL <a class="code" href="classEigen_1_1LDLT.html#a1c29cf5110c180a8fc5da40096822ed1">matrixL</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LDLT is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;      <span class="keywordflow">return</span> Traits::getL(m_matrix);</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    }</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160; </div>
<div class="line"><a name="l00166"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a0779d1ee8b62a8a97275dc36db340a35">  166</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1Transpositions.html">TranspositionType</a>&amp; <a class="code" href="classEigen_1_1LDLT.html#a0779d1ee8b62a8a97275dc36db340a35">transpositionsP</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LDLT is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;      <span class="keywordflow">return</span> m_transpositions;</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;    }</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160; </div>
<div class="line"><a name="l00173"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a1d536082297052c96f074c5e208bb7a8">  173</a></span>&#160;    <span class="keyword">inline</span> <a class="code" href="classEigen_1_1Diagonal.html">Diagonal&lt;const MatrixType&gt;</a> <a class="code" href="classEigen_1_1LDLT.html#a1d536082297052c96f074c5e208bb7a8">vectorD</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LDLT is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;      <span class="keywordflow">return</span> m_matrix.diagonal();</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    }</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160; </div>
<div class="line"><a name="l00180"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#aa1294edd3e62b4b1906918abc75ae50e">  180</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1LDLT.html#aa1294edd3e62b4b1906918abc75ae50e">isPositive</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LDLT is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;      <span class="keywordflow">return</span> m_sign == internal::PositiveSemiDef || m_sign == internal::ZeroSign;</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    }</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160; </div>
<div class="line"><a name="l00187"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a87fc4b3b96a1f432374541defad416f9">  187</a></span>&#160;    <span class="keyword">inline</span> <span class="keywordtype">bool</span> <a class="code" href="classEigen_1_1LDLT.html#a87fc4b3b96a1f432374541defad416f9">isNegative</a>(<span class="keywordtype">void</span>)<span class="keyword"> const</span></div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LDLT is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;      <span class="keywordflow">return</span> m_sign == internal::NegativeSemiDef || m_sign == internal::ZeroSign;</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;    }</div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160; </div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="preprocessor">    #ifdef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Rhs&gt;</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1Solve.html">Solve&lt;LDLT, Rhs&gt;</a></div>
<div class="line"><a name="l00211"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a20cfad0f8808c84d150d1f90abe1fc87">  211</a></span>&#160;    <a class="code" href="classEigen_1_1LDLT.html#a20cfad0f8808c84d150d1f90abe1fc87">solve</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Rhs&gt;</a>&amp; b) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;<span class="preprocessor">    #endif</span></div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160; </div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    <span class="keywordtype">bool</span> solveInPlace(<a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Derived&gt;</a> &amp;bAndX) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160; </div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;    <a class="code" href="classEigen_1_1LDLT.html">LDLT</a>&amp; compute(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; matrix);</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160; </div>
<div class="line"><a name="l00223"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a69bc9dfd866eab90646ca7b74e52c8bc">  223</a></span>&#160;    RealScalar <a class="code" href="classEigen_1_1LDLT.html#a69bc9dfd866eab90646ca7b74e52c8bc">rcond</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LDLT is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;      <span class="keywordflow">return</span> internal::rcond_estimate_helper(m_l1_norm, *<span class="keyword">this</span>);</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    }</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;    <span class="keyword">template</span> &lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;    <a class="code" href="classEigen_1_1LDLT.html">LDLT</a>&amp; rankUpdate(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Derived&gt;</a>&amp; w, <span class="keyword">const</span> RealScalar&amp; alpha=1);</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160; </div>
<div class="line"><a name="l00236"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a3b8250ff102497021676df9f8cb76113">  236</a></span>&#160;    <span class="keyword">inline</span> <span class="keyword">const</span> MatrixType&amp; <a class="code" href="classEigen_1_1LDLT.html#a3b8250ff102497021676df9f8cb76113">matrixLDLT</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LDLT is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;      <span class="keywordflow">return</span> m_matrix;</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;    }</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160; </div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;    MatrixType <a class="code" href="classEigen_1_1LDLT.html#adf2c9a2939f6c5f4e36a94d99d4aa49f">reconstructedMatrix</a>() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160; </div>
<div class="line"><a name="l00249"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#af4fd7733fd47bc76d49d8dde08494195">  249</a></span>&#160;    <span class="keyword">const</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT</a>&amp; <a class="code" href="classEigen_1_1LDLT.html#af4fd7733fd47bc76d49d8dde08494195">adjoint</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> *<span class="keyword">this</span>; }</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160; </div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;    EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_CONSTEXPR <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rows() const EIGEN_NOEXCEPT { <span class="keywordflow">return</span> m_matrix.rows(); }</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;    EIGEN_DEVICE_FUNC <span class="keyword">inline</span> EIGEN_CONSTEXPR <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> cols() const EIGEN_NOEXCEPT { <span class="keywordflow">return</span> m_matrix.cols(); }</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160; </div>
<div class="line"><a name="l00259"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#ae24d5a022e1c09d5afa0e84c356b854e">  259</a></span>&#160;    <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> <a class="code" href="classEigen_1_1LDLT.html#ae24d5a022e1c09d5afa0e84c356b854e">info</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;      eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LDLT is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;      <span class="keywordflow">return</span> m_info;</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;    }</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160; </div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;<span class="preprocessor">    #ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;    <span class="keyword">template</span>&lt;<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;    <span class="keywordtype">void</span> _solve_impl(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160; </div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;    <span class="keyword">template</span>&lt;<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;    <span class="keywordtype">void</span> _solve_impl_transposed(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;<span class="preprocessor">    #endif</span></div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160; </div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160; </div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;    EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160; </div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160;    </div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;    MatrixType m_matrix;</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;    RealScalar m_l1_norm;</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160;    TranspositionType m_transpositions;</div>
<div class="line"><a name="l00286"></a><span class="lineno">  286</span>&#160;    TmpMatrixType m_temporary;</div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;    internal::SignMatrix m_sign;</div>
<div class="line"><a name="l00288"></a><span class="lineno">  288</span>&#160;    <span class="keywordtype">bool</span> m_isInitialized;</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;    <a class="code" href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">ComputationInfo</a> m_info;</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;};</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160; </div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160; </div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">int</span> UpLo&gt; <span class="keyword">struct </span>ldlt_inplace;</div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160; </div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>ldlt_inplace&lt;<a class="code" href="group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdaf581029282d421eee5aae14238c6f749">Lower</a>&gt;</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;{</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> TranspositionType, <span class="keyword">typename</span> Workspace&gt;</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">bool</span> unblocked(MatrixType&amp; mat, TranspositionType&amp; transpositions, Workspace&amp; temp, SignMatrix&amp; <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a>)</div>
<div class="line"><a name="l00300"></a><span class="lineno">  300</span>&#160;  {</div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;    <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00302"></a><span class="lineno">  302</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> TranspositionType::StorageIndex IndexType;</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;    eigen_assert(mat.rows()==mat.cols());</div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;    <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> size = mat.rows();</div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160;    <span class="keywordtype">bool</span> found_zero_pivot = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;    <span class="keywordtype">bool</span> ret = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160; </div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;    <span class="keywordflow">if</span> (size &lt;= 1)</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160;    {</div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;      transpositions.setIdentity();</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160;      <span class="keywordflow">if</span>(size==0) <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> = ZeroSign;</div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span> (numext::real(mat.coeff(0,0)) &gt; <span class="keyword">static_cast&lt;</span>RealScalar<span class="keyword">&gt;</span>(0) ) <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> = PositiveSemiDef;</div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span> (numext::real(mat.coeff(0,0)) &lt; <span class="keyword">static_cast&lt;</span>RealScalar<span class="keyword">&gt;</span>(0)) <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> = NegativeSemiDef;</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160;      <span class="keywordflow">else</span> <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> = ZeroSign;</div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;      <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;    }</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160; </div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> k = 0; k &lt; size; ++k)</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;    {</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;      <span class="comment">// Find largest diagonal element</span></div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> index_of_biggest_in_corner;</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;      mat.diagonal().tail(size-k).cwiseAbs().maxCoeff(&amp;index_of_biggest_in_corner);</div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;      index_of_biggest_in_corner += k;</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160; </div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;      transpositions.coeffRef(k) = IndexType(index_of_biggest_in_corner);</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160;      <span class="keywordflow">if</span>(k != index_of_biggest_in_corner)</div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;      {</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;        <span class="comment">// apply the transposition while taking care to consider only</span></div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;        <span class="comment">// the lower triangular part</span></div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160;        <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> s = size-index_of_biggest_in_corner-1; <span class="comment">// trailing size after the biggest element</span></div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;        mat.row(k).head(k).swap(mat.row(index_of_biggest_in_corner).head(k));</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;        mat.col(k).tail(s).swap(mat.col(index_of_biggest_in_corner).tail(s));</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;        std::swap(mat.coeffRef(k,k),mat.coeffRef(index_of_biggest_in_corner,index_of_biggest_in_corner));</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160;        <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i=k+1;i&lt;index_of_biggest_in_corner;++i)</div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;        {</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;          Scalar tmp = mat.coeffRef(i,k);</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;          mat.coeffRef(i,k) = numext::conj(mat.coeffRef(index_of_biggest_in_corner,i));</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;          mat.coeffRef(index_of_biggest_in_corner,i) = numext::conj(tmp);</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;        }</div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;        <span class="keywordflow">if</span>(NumTraits&lt;Scalar&gt;::IsComplex)</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160;          mat.coeffRef(index_of_biggest_in_corner,k) = numext::conj(mat.coeff(index_of_biggest_in_corner,k));</div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;      }</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160; </div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;      <span class="comment">// partition the matrix:</span></div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;      <span class="comment">//       A00 |  -  |  -</span></div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;      <span class="comment">// lu  = A10 | A11 |  -</span></div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;      <span class="comment">//       A20 | A21 | A22</span></div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rs = size - k - 1;</div>
<div class="line"><a name="l00351"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a0ecf058a0727a4cab8b42d79e95072e1">  351</a></span>&#160;      <a class="code" href="classEigen_1_1Block.html">Block&lt;MatrixType,Dynamic,1&gt;</a> A21(mat,k+1,k,rs,1);</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;      <a class="code" href="classEigen_1_1Block.html">Block&lt;MatrixType,1,Dynamic&gt;</a> A10(mat,k,0,1,k);</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160;      <a class="code" href="classEigen_1_1Block.html">Block&lt;MatrixType,Dynamic,Dynamic&gt;</a> A20(mat,k+1,0,rs,k);</div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160; </div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;      <span class="keywordflow">if</span>(k&gt;0)</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;      {</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160;        temp.head(k) = mat.diagonal().real().head(k).asDiagonal() * A10.adjoint();</div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;        mat.coeffRef(k,k) -= (A10 * temp.head(k)).value();</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;        <span class="keywordflow">if</span>(rs&gt;0)</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;          A21.noalias() -= A20 * temp.head(k);</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160;      }</div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160; </div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;      <span class="comment">// In some previous versions of Eigen (e.g., 3.2.1), the scaling was omitted if the pivot</span></div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;      <span class="comment">// was smaller than the cutoff value. However, since LDLT is not rank-revealing</span></div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;      <span class="comment">// we should only make sure that we do not introduce INF or NaN values.</span></div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;      <span class="comment">// Remark that LAPACK also uses 0 as the cutoff value.</span></div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;      RealScalar realAkk = numext::real(mat.coeffRef(k,k));</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160;      <span class="keywordtype">bool</span> pivot_is_valid = (<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(realAkk) &gt; RealScalar(0));</div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160; </div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;      <span class="keywordflow">if</span>(k==0 &amp;&amp; !pivot_is_valid)</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;      {</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;        <span class="comment">// The entire diagonal is zero, there is nothing more to do</span></div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;        <span class="comment">// except filling the transpositions, and checking whether the matrix is zero.</span></div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;        <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> = ZeroSign;</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;        <span class="keywordflow">for</span>(<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j&lt;size; ++j)</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;        {</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160;          transpositions.coeffRef(j) = IndexType(j);</div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;          ret = ret &amp;&amp; (mat.col(j).tail(size-j-1).array()==Scalar(0)).<a class="code" href="group__Core__Module.html#ga4abe6022fbef6cda264ef2947a2be1a9">all</a>();</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;        }</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;        <span class="keywordflow">return</span> ret;</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160;      }</div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160; </div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;      <span class="keywordflow">if</span>((rs&gt;0) &amp;&amp; pivot_is_valid)</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;        A21 /= realAkk;</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span>(rs&gt;0)</div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;        ret = ret &amp;&amp; (A21.array()==Scalar(0)).<a class="code" href="group__Core__Module.html#ga4abe6022fbef6cda264ef2947a2be1a9">all</a>();</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160; </div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;      <span class="keywordflow">if</span>(found_zero_pivot &amp;&amp; pivot_is_valid) ret = <span class="keyword">false</span>; <span class="comment">// factorization failed</span></div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;      <span class="keywordflow">else</span> <span class="keywordflow">if</span>(!pivot_is_valid) found_zero_pivot = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160; </div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;      <span class="keywordflow">if</span> (<a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> == PositiveSemiDef) {</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;        <span class="keywordflow">if</span> (realAkk &lt; <span class="keyword">static_cast&lt;</span>RealScalar<span class="keyword">&gt;</span>(0)) <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> = Indefinite;</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;      } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> == NegativeSemiDef) {</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;        <span class="keywordflow">if</span> (realAkk &gt; <span class="keyword">static_cast&lt;</span>RealScalar<span class="keyword">&gt;</span>(0)) <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> = Indefinite;</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;      } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (<a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> == ZeroSign) {</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;        <span class="keywordflow">if</span> (realAkk &gt; <span class="keyword">static_cast&lt;</span>RealScalar<span class="keyword">&gt;</span>(0)) <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> = PositiveSemiDef;</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;        <span class="keywordflow">else</span> <span class="keywordflow">if</span> (realAkk &lt; <span class="keyword">static_cast&lt;</span>RealScalar<span class="keyword">&gt;</span>(0)) <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a> = NegativeSemiDef;</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;      }</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;    }</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160; </div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    <span class="keywordflow">return</span> ret;</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;  }</div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160; </div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;  <span class="comment">// Reference for the algorithm: Davis and Hager, &quot;Multiple Rank</span></div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;  <span class="comment">// Modifications of a Sparse Cholesky Factorization&quot; (Algorithm 1)</span></div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;  <span class="comment">// Trivial rearrangements of their computations (Timothy E. Holy)</span></div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160;  <span class="comment">// allow their algorithm to work for rank-1 updates even if the</span></div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;  <span class="comment">// original matrix is not of full rank.</span></div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;  <span class="comment">// Here only rank-1 updates are implemented, to reduce the</span></div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160;  <span class="comment">// requirement for intermediate storage and improve accuracy</span></div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> WDerived&gt;</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">bool</span> updateInPlace(MatrixType&amp; mat, MatrixBase&lt;WDerived&gt;&amp; w, <span class="keyword">const</span> <span class="keyword">typename</span> MatrixType::RealScalar&amp; sigma=1)</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;  {</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160;    <span class="keyword">using</span> numext::isfinite;</div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160; </div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> size = mat.rows();</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;    eigen_assert(mat.cols() == size &amp;&amp; w.size()==size);</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160; </div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;    RealScalar alpha = 1;</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160; </div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;    <span class="comment">// Apply the update</span></div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> j = 0; j &lt; size; j++)</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;    {</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;      <span class="comment">// Check for termination due to an original decomposition of low-rank</span></div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;      <span class="keywordflow">if</span> (!(<a class="code" href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">isfinite</a>)(alpha))</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;        <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160; </div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;      <span class="comment">// Update the diagonal terms</span></div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;      RealScalar dj = numext::real(mat.coeff(j,j));</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;      Scalar wj = w.coeff(j);</div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;      RealScalar swj2 = sigma*numext::abs2(wj);</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;      RealScalar gamma = dj*alpha + swj2;</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160; </div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;      mat.coeffRef(j,j) += swj2/alpha;</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;      alpha += swj2/dj;</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160; </div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160; </div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;      <span class="comment">// Update the terms of L</span></div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;      <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> rs = size-j-1;</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160;      w.tail(rs) -= wj * mat.col(j).tail(rs);</div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;      <span class="keywordflow">if</span>(!numext::is_exactly_zero(gamma))</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;        mat.col(j).tail(rs) += (sigma*numext::conj(wj)/gamma)*w.tail(rs);</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    }</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160;    <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;  }</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160; </div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> TranspositionType, <span class="keyword">typename</span> Workspace, <span class="keyword">typename</span> WType&gt;</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;  <span class="keyword">static</span> <span class="keywordtype">bool</span> update(MatrixType&amp; mat, <span class="keyword">const</span> TranspositionType&amp; transpositions, Workspace&amp; tmp, <span class="keyword">const</span> WType&amp; w, <span class="keyword">const</span> <span class="keyword">typename</span> MatrixType::RealScalar&amp; sigma=1)</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;  {</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;    <span class="comment">// Apply the permutation to the input w</span></div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;    tmp = transpositions * w;</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160; </div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;    <span class="keywordflow">return</span> ldlt_inplace&lt;Lower&gt;::updateInPlace(mat,tmp,sigma);</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;  }</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;};</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160; </div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;<span class="keyword">template</span>&lt;&gt; <span class="keyword">struct </span>ldlt_inplace&lt;<a class="code" href="group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1">Upper</a>&gt;</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;{</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> TranspositionType, <span class="keyword">typename</span> Workspace&gt;</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE <span class="keywordtype">bool</span> unblocked(MatrixType&amp; mat, TranspositionType&amp; transpositions, Workspace&amp; temp, SignMatrix&amp; <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a>)</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;  {</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;    Transpose&lt;MatrixType&gt; matt(mat);</div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;    <span class="keywordflow">return</span> ldlt_inplace&lt;Lower&gt;::unblocked(matt, transpositions, temp, <a class="code" href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">sign</a>);</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;  }</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160; </div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;  <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> TranspositionType, <span class="keyword">typename</span> Workspace, <span class="keyword">typename</span> WType&gt;</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;  <span class="keyword">static</span> EIGEN_STRONG_INLINE <span class="keywordtype">bool</span> update(MatrixType&amp; mat, TranspositionType&amp; transpositions, Workspace&amp; tmp, WType&amp; w, <span class="keyword">const</span> <span class="keyword">typename</span> MatrixType::RealScalar&amp; sigma=1)</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;  {</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160;    Transpose&lt;MatrixType&gt; matt(mat);</div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;    <span class="keywordflow">return</span> ldlt_inplace&lt;Lower&gt;::update(matt, transpositions, tmp, w.conjugate(), sigma);</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;  }</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;};</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160; </div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt; <span class="keyword">struct </span>LDLT_Traits&lt;MatrixType,<a class="code" href="group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdaf581029282d421eee5aae14238c6f749">Lower</a>&gt;</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;{</div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">const</span> TriangularView&lt;const MatrixType, UnitLower&gt; MatrixL;</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">const</span> TriangularView&lt;const typename MatrixType::AdjointReturnType, UnitUpper&gt; MatrixU;</div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> MatrixL getL(<span class="keyword">const</span> MatrixType&amp; m) { <span class="keywordflow">return</span> MatrixL(m); }</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> MatrixU getU(<span class="keyword">const</span> MatrixType&amp; m) { <span class="keywordflow">return</span> MatrixU(m.adjoint()); }</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160;};</div>
<div class="line"><a name="l00483"></a><span class="lineno">  483</span>&#160; </div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType&gt; <span class="keyword">struct </span>LDLT_Traits&lt;MatrixType,<a class="code" href="group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1">Upper</a>&gt;</div>
<div class="line"><a name="l00485"></a><span class="lineno">  485</span>&#160;{</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">const</span> TriangularView&lt;const typename MatrixType::AdjointReturnType, UnitLower&gt; MatrixL;</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">const</span> TriangularView&lt;const MatrixType, UnitUpper&gt; MatrixU;</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> MatrixL getL(<span class="keyword">const</span> MatrixType&amp; m) { <span class="keywordflow">return</span> MatrixL(m.adjoint()); }</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160;  <span class="keyword">static</span> <span class="keyword">inline</span> MatrixU getU(<span class="keyword">const</span> MatrixType&amp; m) { <span class="keywordflow">return</span> MatrixU(m); }</div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;};</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160; </div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;} <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160; </div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> UpLo_&gt;</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> InputType&gt;</div>
<div class="line"><a name="l00498"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a18589fe69cc1286c3da6ad894813899c">  498</a></span>&#160;<a class="code" href="classEigen_1_1LDLT.html">LDLT&lt;MatrixType,UpLo_&gt;</a>&amp; <a class="code" href="classEigen_1_1LDLT.html">LDLT&lt;MatrixType,UpLo_&gt;::compute</a>(<span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html">EigenBase&lt;InputType&gt;</a>&amp; a)</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;{</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;  eigen_assert(a.<a class="code" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>()==a.<a class="code" href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>());</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> size = a.<a class="code" href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>();</div>
<div class="line"><a name="l00502"></a><span class="lineno">  502</span>&#160; </div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;  m_matrix = a.<a class="code" href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">derived</a>();</div>
<div class="line"><a name="l00504"></a><span class="lineno">  504</span>&#160; </div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;  <span class="comment">// Compute matrix L1 norm = max abs column sum.</span></div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;  m_l1_norm = RealScalar(0);</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;  <span class="comment">// TODO move this code to SelfAdjointView</span></div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> col = 0; col &lt; size; ++col) {</div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;    RealScalar abs_col_sum;</div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;    <span class="keywordflow">if</span> (UpLo_ == <a class="code" href="group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdaf581029282d421eee5aae14238c6f749">Lower</a>)</div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;      abs_col_sum = m_matrix.col(col).tail(size - col).template lpNorm&lt;1&gt;() + m_matrix.row(col).head(col).template lpNorm&lt;1&gt;();</div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;      abs_col_sum = m_matrix.col(col).head(col).template lpNorm&lt;1&gt;() + m_matrix.row(col).tail(size - col).template lpNorm&lt;1&gt;();</div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160;    <span class="keywordflow">if</span> (abs_col_sum &gt; m_l1_norm)</div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;      m_l1_norm = abs_col_sum;</div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160;  }</div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160; </div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;  m_transpositions.resize(size);</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;  m_isInitialized = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160;  m_temporary.resize(size);</div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;  m_sign = internal::ZeroSign;</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160; </div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;  m_info = internal::ldlt_inplace&lt;UpLo&gt;::unblocked(m_matrix, m_transpositions, m_temporary, m_sign) ? <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a> : <a class="code" href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b">NumericalIssue</a>;</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160; </div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;}</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160; </div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> UpLo_&gt;</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00536"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#a21a4d19e6c079967ee96c808a8e91d68">  536</a></span>&#160;<a class="code" href="classEigen_1_1LDLT.html">LDLT&lt;MatrixType,UpLo_&gt;</a>&amp; <a class="code" href="classEigen_1_1LDLT.html">LDLT&lt;MatrixType,UpLo_&gt;::rankUpdate</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Derived&gt;</a>&amp; w, <span class="keyword">const</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT&lt;MatrixType,UpLo_&gt;::RealScalar</a>&amp; sigma)</div>
<div class="line"><a name="l00537"></a><span class="lineno">  537</span>&#160;{</div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> TranspositionType::StorageIndex IndexType;</div>
<div class="line"><a name="l00539"></a><span class="lineno">  539</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> size = w.<a class="code" href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>();</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;  <span class="keywordflow">if</span> (m_isInitialized)</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;  {</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160;    eigen_assert(m_matrix.rows()==size);</div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;  }</div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;  {</div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;    m_matrix.resize(size,size);</div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160;    m_matrix.setZero();</div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;    m_transpositions.resize(size);</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;    <span class="keywordflow">for</span> (<a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> i = 0; i &lt; size; i++)</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;      m_transpositions.coeffRef(i) = IndexType(i);</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;    m_temporary.resize(size);</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160;    m_sign = sigma&gt;=0 ? internal::PositiveSemiDef : internal::NegativeSemiDef;</div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;    m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;  }</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160; </div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;  internal::ldlt_inplace&lt;UpLo&gt;::update(m_matrix, m_transpositions, m_temporary, w, sigma);</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160; </div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;  <span class="keywordflow">return</span> *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;}</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160; </div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;<span class="preprocessor">#ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> UpLo_&gt;</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160;<span class="keywordtype">void</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT&lt;MatrixType_,UpLo_&gt;::_solve_impl</a>(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;  _solve_impl_transposed&lt;true&gt;(rhs, dst);</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;}</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160; </div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType_,<span class="keywordtype">int</span> UpLo_&gt;</div>
<div class="line"><a name="l00570"></a><span class="lineno">  570</span>&#160;<span class="keyword">template</span>&lt;<span class="keywordtype">bool</span> Conjugate, <span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DstType&gt;</div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;<span class="keywordtype">void</span> LDLT&lt;MatrixType_,UpLo_&gt;::_solve_impl_transposed(<span class="keyword">const</span> RhsType &amp;rhs, DstType &amp;dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00572"></a><span class="lineno">  572</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;  <span class="comment">// dst = P b</span></div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;  dst = m_transpositions * rhs;</div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160; </div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;  <span class="comment">// dst = L^-1 (P b)</span></div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;  <span class="comment">// dst = L^-*T (P b)</span></div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;  matrixL().template conjugateIf&lt;!Conjugate&gt;().solveInPlace(dst);</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160; </div>
<div class="line"><a name="l00580"></a><span class="lineno">  580</span>&#160;  <span class="comment">// dst = D^-* (L^-1 P b)</span></div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;  <span class="comment">// dst = D^-1 (L^-*T P b)</span></div>
<div class="line"><a name="l00582"></a><span class="lineno">  582</span>&#160;  <span class="comment">// more precisely, use pseudo-inverse of D (see bug 241)</span></div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;  <span class="keyword">const</span> <span class="keyword">typename</span> Diagonal&lt;const MatrixType&gt;::RealReturnType vecD(vectorD());</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;  <span class="comment">// In some previous versions, tolerance was set to the max of 1/highest (or rather numeric_limits::min())</span></div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;  <span class="comment">// and the maximal diagonal entry * epsilon as motivated by LAPACK&#39;s xGELSS:</span></div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;  <span class="comment">// RealScalar tolerance = numext::maxi(vecD.array().abs().maxCoeff() * NumTraits&lt;RealScalar&gt;::epsilon(),RealScalar(1) / NumTraits&lt;RealScalar&gt;::highest());</span></div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;  <span class="comment">// However, LDLT is not rank revealing, and so adjusting the tolerance wrt to the highest</span></div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;  <span class="comment">// diagonal element is not well justified and leads to numerical issues in some cases.</span></div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;  <span class="comment">// Moreover, Lapack&#39;s xSYTRS routines use 0 for the tolerance.</span></div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;  <span class="comment">// Using numeric_limits::min() gives us more robustness to denormals.</span></div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  RealScalar tolerance = (std::numeric_limits&lt;RealScalar&gt;::min)();</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;  <span class="keywordflow">for</span> (<a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i = 0; i &lt; vecD.size(); ++i)</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;  {</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160;    <span class="keywordflow">if</span>(<a class="code" href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">abs</a>(vecD(i)) &gt; tolerance)</div>
<div class="line"><a name="l00596"></a><span class="lineno">  596</span>&#160;      dst.row(i) /= vecD(i);</div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00598"></a><span class="lineno">  598</span>&#160;      dst.row(i).setZero();</div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;  }</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160; </div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;  <span class="comment">// dst = L^-* (D^-* L^-1 P b)</span></div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;  <span class="comment">// dst = L^-T (D^-1 L^-*T P b)</span></div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;  matrixL().transpose().template conjugateIf&lt;Conjugate&gt;().solveInPlace(dst);</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160; </div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160;  <span class="comment">// dst = P^T (L^-* D^-* L^-1 P b) = A^-1 b</span></div>
<div class="line"><a name="l00606"></a><span class="lineno">  606</span>&#160;  <span class="comment">// dst = P^-T (L^-T D^-1 L^-*T P b) = A^-1 b</span></div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;  dst = m_transpositions.transpose() * dst;</div>
<div class="line"><a name="l00608"></a><span class="lineno">  608</span>&#160;}</div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160; </div>
<div class="line"><a name="l00624"></a><span class="lineno">  624</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType,<span class="keywordtype">int</span> UpLo_&gt;</div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;<span class="keywordtype">bool</span> LDLT&lt;MatrixType,UpLo_&gt;::solveInPlace(MatrixBase&lt;Derived&gt; &amp;bAndX)<span class="keyword"> const</span></div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;  eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LDLT is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;  eigen_assert(m_matrix.rows() == bAndX.rows());</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160; </div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160;  bAndX = this-&gt;solve(bAndX);</div>
<div class="line"><a name="l00632"></a><span class="lineno">  632</span>&#160; </div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00634"></a><span class="lineno">  634</span>&#160;}</div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160; </div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">int</span> UpLo_&gt;</div>
<div class="line"><a name="l00640"></a><span class="lineno"><a class="line" href="classEigen_1_1LDLT.html#adf2c9a2939f6c5f4e36a94d99d4aa49f">  640</a></span>&#160;MatrixType <a class="code" href="classEigen_1_1LDLT.html#adf2c9a2939f6c5f4e36a94d99d4aa49f">LDLT&lt;MatrixType,UpLo_&gt;::reconstructedMatrix</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00641"></a><span class="lineno">  641</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;  eigen_assert(m_isInitialized &amp;&amp; <span class="stringliteral">&quot;LDLT is not initialized.&quot;</span>);</div>
<div class="line"><a name="l00643"></a><span class="lineno">  643</span>&#160;  <span class="keyword">const</span> <a class="code" href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Index</a> size = m_matrix.rows();</div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;  MatrixType res(size,size);</div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160; </div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;  <span class="comment">// P</span></div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;  res.setIdentity();</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;  res = transpositionsP() * res;</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;  <span class="comment">// L^* P</span></div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160;  res = matrixU() * res;</div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;  <span class="comment">// D(L^*P)</span></div>
<div class="line"><a name="l00652"></a><span class="lineno">  652</span>&#160;  res = vectorD().real().asDiagonal() * res;</div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;  <span class="comment">// L(DL^*P)</span></div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;  res = matrixL() * res;</div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;  <span class="comment">// P^T (LDL^*P)</span></div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;  res = transpositionsP().transpose() * res;</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160; </div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;  <span class="keywordflow">return</span> res;</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;}</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160; </div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> UpLo&gt;</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;<span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT&lt;typename SelfAdjointView&lt;MatrixType, UpLo&gt;::PlainObject</a>, UpLo&gt;</div>
<div class="line"><a name="l00667"></a><span class="lineno"><a class="line" href="classEigen_1_1SelfAdjointView.html#a644155eef17b37c95d85b9f65bb49ac4">  667</a></span>&#160;<a class="code" href="classEigen_1_1SelfAdjointView.html#a644155eef17b37c95d85b9f65bb49ac4">SelfAdjointView&lt;MatrixType, UpLo&gt;::ldlt</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT&lt;PlainObject,UpLo&gt;</a>(m_matrix);</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160;}</div>
<div class="line"><a name="l00671"></a><span class="lineno">  671</span>&#160; </div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> Derived&gt;</div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;<span class="keyword">inline</span> <span class="keyword">const</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT&lt;typename MatrixBase&lt;Derived&gt;::PlainObject</a>&gt;</div>
<div class="line"><a name="l00678"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a0ecf058a0727a4cab8b42d79e95072e1">  678</a></span>&#160;<a class="code" href="classEigen_1_1MatrixBase.html#a0ecf058a0727a4cab8b42d79e95072e1">MatrixBase&lt;Derived&gt;::ldlt</a>()<span class="keyword"> const</span></div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;<span class="keyword"></span>{</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;  <span class="keywordflow">return</span> <a class="code" href="classEigen_1_1LDLT.html">LDLT&lt;PlainObject&gt;</a>(derived());</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;}</div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160; </div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160; </div>
<div class="line"><a name="l00685"></a><span class="lineno">  685</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_LDLT_H</span></div>
<div class="ttc" id="aclassEigen_1_1Block_html"><div class="ttname"><a href="classEigen_1_1Block.html">Eigen::Block</a></div><div class="ttdoc">Expression of a fixed-size or dynamic-size block.</div><div class="ttdef"><b>Definition:</b> Block.h:107</div></div>
<div class="ttc" id="aclassEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4_html_ac22eb0695d00edd7d4a3b2d0a98b81c2"><div class="ttname"><a href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">Eigen::DenseCoeffsBase&lt; Derived, DirectWriteAccessors &gt;::rows</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:62</div></div>
<div class="ttc" id="aclassEigen_1_1Diagonal_html"><div class="ttname"><a href="classEigen_1_1Diagonal.html">Eigen::Diagonal</a></div><div class="ttdoc">Expression of a diagonal/subdiagonal/superdiagonal in a matrix.</div><div class="ttdef"><b>Definition:</b> Diagonal.h:67</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html"><div class="ttname"><a href="classEigen_1_1LDLT.html">Eigen::LDLT</a></div><div class="ttdoc">Robust Cholesky decomposition of a matrix with pivoting.</div><div class="ttdef"><b>Definition:</b> LDLT.h:63</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_a0779d1ee8b62a8a97275dc36db340a35"><div class="ttname"><a href="classEigen_1_1LDLT.html#a0779d1ee8b62a8a97275dc36db340a35">Eigen::LDLT::transpositionsP</a></div><div class="ttdeci">const TranspositionType &amp; transpositionsP() const</div><div class="ttdef"><b>Definition:</b> LDLT.h:166</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_a1c29cf5110c180a8fc5da40096822ed1"><div class="ttname"><a href="classEigen_1_1LDLT.html#a1c29cf5110c180a8fc5da40096822ed1">Eigen::LDLT::matrixL</a></div><div class="ttdeci">Traits::MatrixL matrixL() const</div><div class="ttdef"><b>Definition:</b> LDLT.h:158</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_a1d536082297052c96f074c5e208bb7a8"><div class="ttname"><a href="classEigen_1_1LDLT.html#a1d536082297052c96f074c5e208bb7a8">Eigen::LDLT::vectorD</a></div><div class="ttdeci">Diagonal&lt; const MatrixType &gt; vectorD() const</div><div class="ttdef"><b>Definition:</b> LDLT.h:173</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_a20cfad0f8808c84d150d1f90abe1fc87"><div class="ttname"><a href="classEigen_1_1LDLT.html#a20cfad0f8808c84d150d1f90abe1fc87">Eigen::LDLT::solve</a></div><div class="ttdeci">const Solve&lt; LDLT, Rhs &gt; solve(const MatrixBase&lt; Rhs &gt; &amp;b) const</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_a3b8250ff102497021676df9f8cb76113"><div class="ttname"><a href="classEigen_1_1LDLT.html#a3b8250ff102497021676df9f8cb76113">Eigen::LDLT::matrixLDLT</a></div><div class="ttdeci">const MatrixType &amp; matrixLDLT() const</div><div class="ttdef"><b>Definition:</b> LDLT.h:236</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_a3ed6b348086c7b4c117dbff35be1a16d"><div class="ttname"><a href="classEigen_1_1LDLT.html#a3ed6b348086c7b4c117dbff35be1a16d">Eigen::LDLT::setZero</a></div><div class="ttdeci">void setZero()</div><div class="ttdef"><b>Definition:</b> LDLT.h:145</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_a69bc9dfd866eab90646ca7b74e52c8bc"><div class="ttname"><a href="classEigen_1_1LDLT.html#a69bc9dfd866eab90646ca7b74e52c8bc">Eigen::LDLT::rcond</a></div><div class="ttdeci">RealScalar rcond() const</div><div class="ttdef"><b>Definition:</b> LDLT.h:223</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_a87fc4b3b96a1f432374541defad416f9"><div class="ttname"><a href="classEigen_1_1LDLT.html#a87fc4b3b96a1f432374541defad416f9">Eigen::LDLT::isNegative</a></div><div class="ttdeci">bool isNegative(void) const</div><div class="ttdef"><b>Definition:</b> LDLT.h:187</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_a9ab5fbbe154dd5b43fe272126d69411f"><div class="ttname"><a href="classEigen_1_1LDLT.html#a9ab5fbbe154dd5b43fe272126d69411f">Eigen::LDLT::LDLT</a></div><div class="ttdeci">LDLT()</div><div class="ttdoc">Default Constructor.</div><div class="ttdef"><b>Definition:</b> LDLT.h:87</div></div>
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<div class="ttc" id="aclassEigen_1_1LDLT_html_ab45453a84ebb985cb0d1d9128b7af18d"><div class="ttname"><a href="classEigen_1_1LDLT.html#ab45453a84ebb985cb0d1d9128b7af18d">Eigen::LDLT::LDLT</a></div><div class="ttdeci">LDLT(const EigenBase&lt; InputType &gt; &amp;matrix)</div><div class="ttdoc">Constructor with decomposition.</div><div class="ttdef"><b>Definition:</b> LDLT.h:115</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_abd3c8856337dfc7f4df6214b9503dcf2"><div class="ttname"><a href="classEigen_1_1LDLT.html#abd3c8856337dfc7f4df6214b9503dcf2">Eigen::LDLT::LDLT</a></div><div class="ttdeci">LDLT(Index size)</div><div class="ttdoc">Default Constructor with memory preallocation.</div><div class="ttdef"><b>Definition:</b> LDLT.h:100</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_ad2f39b7a2a17c6e982db2e4164b6dd9f"><div class="ttname"><a href="classEigen_1_1LDLT.html#ad2f39b7a2a17c6e982db2e4164b6dd9f">Eigen::LDLT::LDLT</a></div><div class="ttdeci">LDLT(EigenBase&lt; InputType &gt; &amp;matrix)</div><div class="ttdoc">Constructs a LDLT factorization from a given matrix.</div><div class="ttdef"><b>Definition:</b> LDLT.h:132</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_adf2c9a2939f6c5f4e36a94d99d4aa49f"><div class="ttname"><a href="classEigen_1_1LDLT.html#adf2c9a2939f6c5f4e36a94d99d4aa49f">Eigen::LDLT::reconstructedMatrix</a></div><div class="ttdeci">MatrixType reconstructedMatrix() const</div><div class="ttdef"><b>Definition:</b> LDLT.h:640</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_ae24d5a022e1c09d5afa0e84c356b854e"><div class="ttname"><a href="classEigen_1_1LDLT.html#ae24d5a022e1c09d5afa0e84c356b854e">Eigen::LDLT::info</a></div><div class="ttdeci">ComputationInfo info() const</div><div class="ttdoc">Reports whether previous computation was successful.</div><div class="ttdef"><b>Definition:</b> LDLT.h:259</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_ae8be83b613c7fad1ad5d0a2b44c483e0"><div class="ttname"><a href="classEigen_1_1LDLT.html#ae8be83b613c7fad1ad5d0a2b44c483e0">Eigen::LDLT::matrixU</a></div><div class="ttdeci">Traits::MatrixU matrixU() const</div><div class="ttdef"><b>Definition:</b> LDLT.h:151</div></div>
<div class="ttc" id="aclassEigen_1_1LDLT_html_af4fd7733fd47bc76d49d8dde08494195"><div class="ttname"><a href="classEigen_1_1LDLT.html#af4fd7733fd47bc76d49d8dde08494195">Eigen::LDLT::adjoint</a></div><div class="ttdeci">const LDLT &amp; adjoint() const</div><div class="ttdef"><b>Definition:</b> LDLT.h:249</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions.</div><div class="ttdef"><b>Definition:</b> MatrixBase.h:52</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a0ecf058a0727a4cab8b42d79e95072e1"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a0ecf058a0727a4cab8b42d79e95072e1">Eigen::MatrixBase::ldlt</a></div><div class="ttdeci">const LDLT&lt; PlainObject &gt; ldlt() const</div><div class="ttdef"><b>Definition:</b> LDLT.h:678</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix&lt; Scalar, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime, 1 &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1PermutationMatrix_html"><div class="ttname"><a href="classEigen_1_1PermutationMatrix.html">Eigen::PermutationMatrix&lt; RowsAtCompileTime, MaxRowsAtCompileTime &gt;</a></div></div>
<div class="ttc" id="aclassEigen_1_1SelfAdjointView_html_a644155eef17b37c95d85b9f65bb49ac4"><div class="ttname"><a href="classEigen_1_1SelfAdjointView.html#a644155eef17b37c95d85b9f65bb49ac4">Eigen::SelfAdjointView::ldlt</a></div><div class="ttdeci">const LDLT&lt; PlainObject, UpLo &gt; ldlt() const</div><div class="ttdef"><b>Definition:</b> LDLT.h:667</div></div>
<div class="ttc" id="aclassEigen_1_1Solve_html"><div class="ttname"><a href="classEigen_1_1Solve.html">Eigen::Solve</a></div><div class="ttdoc">Pseudo expression representing a solving operation.</div><div class="ttdef"><b>Definition:</b> Solve.h:65</div></div>
<div class="ttc" id="aclassEigen_1_1SolverBase_html"><div class="ttname"><a href="classEigen_1_1SolverBase.html">Eigen::SolverBase</a></div><div class="ttdoc">A base class for matrix decomposition and solvers.</div><div class="ttdef"><b>Definition:</b> SolverBase.h:71</div></div>
<div class="ttc" id="aclassEigen_1_1SolverBase_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="classEigen_1_1SolverBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::SolverBase&lt; LDLT&lt; MatrixType_, UpLo_ &gt; &gt;::derived</a></div><div class="ttdeci">LDLT&lt; MatrixType_, UpLo_ &gt; &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="aclassEigen_1_1Transpositions_html"><div class="ttname"><a href="classEigen_1_1Transpositions.html">Eigen::Transpositions&lt; RowsAtCompileTime, MaxRowsAtCompileTime &gt;</a></div></div>
<div class="ttc" id="agroup__Core__Module_html_ga4abe6022fbef6cda264ef2947a2be1a9"><div class="ttname"><a href="group__Core__Module.html#ga4abe6022fbef6cda264ef2947a2be1a9">Eigen::placeholders::all</a></div><div class="ttdeci">static const Eigen::internal::all_t all</div><div class="ttdef"><b>Definition:</b> IndexedViewHelper.h:189</div></div>
<div class="ttc" id="agroup__enums_html_ga85fad7b87587764e5cf6b513a9e0ee5e"><div class="ttname"><a href="group__enums.html#ga85fad7b87587764e5cf6b513a9e0ee5e">Eigen::ComputationInfo</a></div><div class="ttdeci">ComputationInfo</div><div class="ttdef"><b>Definition:</b> Constants.h:442</div></div>
<div class="ttc" id="agroup__enums_html_gga39e3366ff5554d731e7dc8bb642f83cdaf581029282d421eee5aae14238c6f749"><div class="ttname"><a href="group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdaf581029282d421eee5aae14238c6f749">Eigen::Lower</a></div><div class="ttdeci">@ Lower</div><div class="ttdef"><b>Definition:</b> Constants.h:211</div></div>
<div class="ttc" id="agroup__enums_html_gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1"><div class="ttname"><a href="group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1">Eigen::Upper</a></div><div class="ttdeci">@ Upper</div><div class="ttdef"><b>Definition:</b> Constants.h:213</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea1c6e20706575a629b27a105f07f1883b">Eigen::NumericalIssue</a></div><div class="ttdeci">@ NumericalIssue</div><div class="ttdef"><b>Definition:</b> Constants.h:446</div></div>
<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf"><div class="ttname"><a href="group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Eigen::Success</a></div><div class="ttdeci">@ Success</div><div class="ttdef"><b>Definition:</b> Constants.h:444</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_a831e88e0403a42d0dfb328d8acd3e56f"><div class="ttname"><a href="namespaceEigen.html#a831e88e0403a42d0dfb328d8acd3e56f">Eigen::sign</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_sign_op&lt; typename Derived::Scalar &gt;, const Derived &gt; sign(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_aba24ec81dec745a00b7f33adead89811"><div class="ttname"><a href="namespaceEigen.html#aba24ec81dec745a00b7f33adead89811">Eigen::isfinite</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_isfinite_op&lt; typename Derived::Scalar &gt;, const Derived &gt; isfinite(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="anamespaceEigen_html_ae27242789e7e62a8c42579b79be59b1a"><div class="ttname"><a href="namespaceEigen.html#ae27242789e7e62a8c42579b79be59b1a">Eigen::abs</a></div><div class="ttdeci">const Eigen::CwiseUnaryOp&lt; Eigen::internal::scalar_abs_op&lt; typename Derived::Scalar &gt;, const Derived &gt; abs(const Eigen::ArrayBase&lt; Derived &gt; &amp;x)</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html"><div class="ttname"><a href="structEigen_1_1EigenBase.html">Eigen::EigenBase</a></div><div class="ttdef"><b>Definition:</b> EigenBase.h:32</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a1fbabe7f12bcbfba3b9a448b1f5e46fa"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a1fbabe7f12bcbfba3b9a448b1f5e46fa">Eigen::EigenBase::derived</a></div><div class="ttdeci">Derived &amp; derived()</div><div class="ttdef"><b>Definition:</b> EigenBase.h:48</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a2d768a9877f5f69f49432d447b552bfe"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a2d768a9877f5f69f49432d447b552bfe">Eigen::EigenBase::cols</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:65</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_a554f30542cc2316add4b1ea0a492ff02"><div class="ttname"><a href="structEigen_1_1EigenBase.html#a554f30542cc2316add4b1ea0a492ff02">Eigen::EigenBase::Index</a></div><div class="ttdeci">Eigen::Index Index</div><div class="ttdoc">The interface type of indices.</div><div class="ttdef"><b>Definition:</b> EigenBase.h:41</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_ac22eb0695d00edd7d4a3b2d0a98b81c2"><div class="ttname"><a href="structEigen_1_1EigenBase.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">Eigen::EigenBase::rows</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:62</div></div>
<div class="ttc" id="astructEigen_1_1EigenBase_html_ae106171b6fefd3f7af108a8283de36c9"><div class="ttname"><a href="structEigen_1_1EigenBase.html#ae106171b6fefd3f7af108a8283de36c9">Eigen::EigenBase::size</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:69</div></div>
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